Skip to main content
SpringerLink
Log in

On an optimal control problem for a hyperbolic partial differential equation

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Existence of solutions is proved for a minimum problem for a distributed-parameter control system described by a linear, hyperbolic partial differential equation. The cost function is an integral depending on boundary controls.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pulvirenti, G.,Su Alcuni Problemi di Teoria dei Controlli Relativi ad una Equazione alle Derivate Parziali di Tipo Iperbolico, Le Matematiche, Vol. 23, No. 2, 1968.

  2. Santagati, G.,Alcuni Problemi di Controllo Ottimo Relativi and una Equazione alle Derivate Parziali di Tipo Iperbolico, Le Matematiche, Vol. 23, No. 2, 1968.

  3. Pulvirenti, G., andSantagati, G.,Controlli Lineari nel Problema di Dirichlet per una Equazione di Tipo Iperbolico, Le Matematiche, Vol. 23, No. 2, 1968.

  4. Pulvirenti, G., andSantagati, G.,Nuovi Contributi alla Teoria dei Controlli per Sistemi Materiali Retti da una Equazione alle Derivate Parziali di Tipo Iperbolico, Le Matematiche, Vol. 24, No. 2, 1969.

  5. Egorov, A. I.,Optimal Processes in Distributed-Parameter Systems and Certain Problems in Invariance Theory, SIAM Journal on Control, Vol. 4, No. 4, 1966.

  6. Cesari, L.,Existence Theorems for Optimal Solutions in Pontryagin and Lagrange Problems, SIAM Journal on Control, Vol. 3, No. 3, 1965.

  7. Cesari, L.,Existence Theorems for Weak and Usual Optimal Solutions in Lagrange Problems with Unilateral Constraints, I, Transactions of the American Mathematical Society, Vol. 124, No. 3, 1966.

  8. Zolezzi, T.,Teoremi di Esistenza nella Teoria dei Controlli Ottimi in Dimensione Finita, Rendiconti del Seminario Matematico della Università di Padova, Vol. 39, 1967.

  9. Pulvirenti, G.,Existence Theorems for an Optimal Control Problem Relative to a Linear Hyperbolic Partial Differential Equation, Journal of Optimization Theory and Applications, Vol. 7, No. 2, 1971.

  10. Hadamard, J.,Le Problème de Cauchy et les Equations aux Dérivées Partielles Linéaires Hyperboliques, Hermann, Paris, 1932.

    Google Scholar 

  11. Browder, F.,Remarks on the Direct Method of the Calculus of Variations, Archive for Rational Mechanics and Analysis, Vol. 20, 1965.

Download references

Author information

Authors and Affiliations

  1. Seminario Matematico, Università di Catania, Catania, Italy

    G. Santagati (Professor of Mathematical Analysis)

Authors
  1. G. Santagati
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by R. Conti

This research was supported by the Consiglio Nazionale delle Ricerche, Rome, Italy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Santagati, G. On an optimal control problem for a hyperbolic partial differential equation. J Optim Theory Appl 7, 1–10 (1971). https://doi.org/10.1007/BF00933588

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00933588

Keywords

Search

Navigation